Abstract
An integrodifferential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered. The local polynomial regression method (LPR) is used to solve this equation. The reliability of this method and the reduction in the size of computational domain give this method a wider applicability. Several representative examples are given to reconfirm the efficiency of these algorithms. The results of applying this theory to the integro-differential equation with time-periodic coefficients reveal that LPR method possesses very high accuracy, adaptability, and efficiency.
Highlights
Most scientific problems in engineering are inherently nonlinear
Numerical results demonstrate that local polynomial fitting method is more accurate, simple, and efficient
The destination of this paper is to use local polynomial regression method for solving integro-differential equations arising in oscillating magnetic fields
Summary
Most scientific problems in engineering are inherently nonlinear. Except a few number of them, majority of nonlinear problems such as complex integro-differential equation do not have analytical solution. Some mathematical methods have been employed to solve different physical differential equations, such as Homotopy perturbation technique by authors [1,2,3,4], Homotopy analysis method given by Dehghan and Shakeri [5], time periodic coefficients by Machado and Tsuchida [6], hysteretic damping used by Chen and You [7], rapidly vanishing convolution kernels by authors [8], Adomian decomposition method by Biazar et al [9] and Biazar [10], operational tau approximation by Dehcheshmeh et al [11], Modified Homotopy Perturbation Method by authors [12], the Tau approximation for the delayed Burgers equation by Khaksar Haghani et al [13], a modified variable separated ordinary differential equation method solving mKdV sinh-Gordon equation by Xie [14], the projective Riccati equation expansion method and variable separation solutions for the nonlinear physical differential equation in physics by Ma [15], and Lagrange-Noether method for solving second-order differential equations by Hui-Bin and Run-Heng [16] They are all proved to have efficiency and utility widely. The destination of this paper is to use local polynomial regression method for solving integro-differential equations arising in oscillating magnetic fields
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